Non‐stationarity in rainfall and temperature in the Murray Darling Basin

Two analyses, one based on multiple regression and the other using the Holt–Winters algorithm, for investigating non-stationarity in environmental time series are presented. They are applied to monthly rainfall and average maximum temperature time series of lengths between 38 and 108 years, from six stations in the Murray Darling Basin and four cities in eastern Australia. The first analysis focuses on the residuals after fitting regression models which allow for seasonal variation, the Pacific Decadal Oscillation (PDO) and the Southern Oscillation Index (SOI). The models provided evidence that rainfall is reduced during periods of negative SOI, and that the interaction between PDO and SOI pronounces this effect during periods of negative PDO. Following this, there was no evidence of any trend in either the PDO or SOI time series. The residuals from this regression were analysed with a cumulative sum (CUSUM) technique, and the statistical significance was assessed using a Monte Carlo method. The residuals were also analysed for volatility, autocorrelation, long-range dependence and spatial correlation. For all ten rainfall and temperature time series, CUSUM plots of the residuals provided evidence of non-stationarity for both temperature and rainfall, after removing seasonal effects and the effects of PDO and SOI. Rainfall was generally lower in the first half of the twentieth century and higher during the second half. However, it decreased again over the last 10 years. This pattern was highlighted with 5-year moving average plots. The residuals for temperature showed a complementary pattern with increases in temperature corresponding to decreased rainfall. The second analysis decomposed the rainfall and temperature time series into random variation about an underlying level, trend and additive seasonal effects and changes in the level; trend and seasonal effects were tracked using a Holt–Winters algorithm. The results of this analysis were qualitatively similar to those of the regression analysis. Copyright © 2010 John Wiley & Sons, Ltd.